TL;DR: The Alien could probably survive for a while without a pressure suit but would definitely suffer long term side effects.
The gravity issue is a problem. Astronauts in space suffer issues of losing the calcium in their bones after long periods of weightlessness, which weakens the bones and would make them brittle and prone to breaking. The gravity of earth being 3 to 4 times less than that of the Alien's home planet could induce the same effects in the aliens, causing long term irreparable damage.
RonJohn's answer about high altitude got me thinking, so I did some research. High altitude is rough on humans because initially there is a stark increase in breathing, and heart-rate in an attempt to compensate for sparseness of oxygen in the air. For obvious reasons, this doesn't do so well for humans who suffer from Hypoxia at higher altitudes without breathing tanks and masks.
For your alien, who can safely increase their blood pressure and heart rate, this might not be an issue as they would be able to get the oxygen that they need without suffering strain on their body the way humans do. After a time, the Alien would likely acclimatize to the earth's atmosphere, and while they wouldn't necessarily have the strength or endurance that they had on their home planet, they would most likely be able to survive.
Now for the gravity issue it might be more of a problem. Astronauts in space suffer issues of losing the calcium in their bones after long periods of weightlessness, which weakens the bones and would make them brittle and prone to breaking. The gravity of earth being 3 to 4 times less than that of the Alien's home planet could induce the same effects in the aliens, causing long term irreparable damage.
References:
https://www.space.com/23017-weightlessness.html https://www2.palomar.edu/anthro/adapt/adapt_3.htm
Edit: I reworked my answer to conform better with site guidelines. Thanks for the heads up Frostfyre.